A matrix-free approach for solving systems of nonlinear equations
Auwal Bala Abubakar, Mohammed Yusuf Waziri · Journal of Modern Methods in Numerical Mathematics · 2016
The computation of the Jacobian, its inverse and $n\times n$ matrix storage requirement in each iteration limits the application of Newton-like method for solving systems of nonlinear equations, because computing the Jacobian entails derivative and to compute its inverse, it must be non-singular. We present an enhancement of a three-step Newton-like method by J. R. Sharma and P. Gupta (2014) where the Jacobian inverse is approximated into a diagonal matrix. Numerical results proved that the proposed method in terms of CPU time and number of iterations compared to the Sharma and Gupta's method is very encouraging.